Abstract
The excess of confidence in logic culminates in logicism, a position common to medieval Scholasticism and modern rationalism. This mistake can best be illustrated by the idea, especially developed by Leibniz, that the lack of contradiction in a concept is a warrant that the corresponding object exists. Certain inconsistencies in Leibniz’s system were corrected by Wolff, whose excesses finally allowed Kant to uncover the logicist fallacy.
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Notes
- 1.
The reader will remark, from this and many other passages of this work, that Nelson thought very highly indeed of the contributions made by Kant towards the identification and prevention of typical fallacies in philosophy. This might lead the reader to expect that Kant was, in Nelson’s view, somehow immune to these fallacies. To show this is not at all the case a brief sample of Kantian fallacies, as identified by Nelson himself, is given in the Appendix.
- 2.
See Pascal (ca. 1657).
- 3.
At the time of these lectures it seems that the term ‘logicism’ had not yet been taken to refer to the doctrine, most closely associated with Frege and Russell, according to which the whole of mathematics could be reduced to logic; see Grattan-Guinness (2000, 3–4, 479 and 501), whose account of the complicated history of the doctrine itself is authoritative. In that sense, Nelson’s usage is probably pioneering, although he clearly meant it much more broadly and polemically (see already Nelson 1908, 1917, where he applies it to epistemology and ethics, respectively).
- 4.
At this point a theme is announced that will recur in these lectures. Fries and Nelson, following Kant’s strictures, and in opposition both to German idealism and to German (nonmathematical) ‘logicians’, distinguished terminologically between a concept (Begriff) and an object (Gegenstand), very much in the way Frege (1892) later did. It is a shame that Nelson died before Frege’s logical views and the much more perspicuous notation they allowed became generally accepted in Germany, to a large extent thanks to the first modern logical treatise (Hilbert and Ackerman 1928). If readers keep this in mind, they will understand certain later passages, especially in Chapters “Lecture V”, “Lecture VI”, “Lecture VII”, “Lecture XII”, “Lecture XV”, “Lecture IX” and “Lecture XXII”. See Footnote 6 in Chapter “Lecture XXII”.
- 5.
See Kant’s essay on ‘the only possible argument for the existence of God’ (1763, Sect. 1, Third Reflection, §6; English version in Walford 1992, 130). The word ‘predicate’ translates the German word Realität, which cannot be translated by ‘reality’, for in the scholastic tradition, to which the Leibnizo-Kantian school terminologically belongs, Realität does not refer either to actual existence or to actually existing things, but rather to the positive features or properties of an object that itself might or might not exist (see Wolff 1736, §243). This is why the modern logical term ‘predicate’ is particularly apt in this context.
- 6.
The German phrase is All der Realitäten, and here again the word Realität is a higher-order term referring to any positive predicate, to a quality or property that an object may have or lack. Although the phrase das All der Realitäten (or rather das All der Realität) stems from Kant, the concept is thoroughly Leibnizian. See Kant, Critique of Pure Reason, A575–576 B603–604, A628, B656. The expression ‘Universal Set’ seems to render the meaning intended in a way that is clearer for contemporary readers.
- 7.
- 8.
See e.g. Baumgarten (1779, §803).
- 9.
He says that in his incomplete and posthumous Treatise on the Improvement of the Understanding, §72. See Morgan (2002: 20).
- 10.
Although the story is decidedly funny, there may have been method in the madness. See Griard (2008).
- 11.
This principle is mentioned by Leibniz on different occasions and in various ways, most famously in his Discourse of Metaphysics and his correspondence with Antoine Arnauld. See e.g. Loemker (1969: 307, 310, 337).
- 12.
See Wolff (1736, §70).
- 13.
See Kant’s Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality of 1763, Third Reflection, §3 (English version in Walford 1992, 267–268).
- 14.
Every definition has the same linguistic form: it associates a chain of words (the definiens) with a given term (the definiendum). The association might be a pure (thoroughly arbitrary) stipulation, as when I say that, from now on, the invented word ‘schmin’ will mean ‘a chimney of pyramidal shape’; or it might have some empirical value, as when a lexicographer explains the meaning that a given word (say, ‘unicorn’) has for a given cultural community. All such definitions are purely nominal, in that the definitions do not imply the existence of an object in the real world that the defined term refers to or of which the defined term might be predicated. The opposite of a nominal definition is a real definition, which either gives directions for the construction of a mathematical object or describes the operations by which we can identify or detect a thing or process. See Footnote 11 in Chapter “Lecture XI”.
- 15.
The phrase ‘necessary and sufficient’ refers to a biconditional. Nelson is talking about a purely logical constraint for definitions, viz that every definition has the form ‘x is F if and only if x is G’, where F is the concept to be defined and G is the concept that defines F. Given any concept F that we want to define, there is usually no unique way to define F. Mathematicians and scientists in general choose among an indefinite number of equivalent definitions the one most suited to the purpose at hand. Observe also that the whole purpose of a definition is to enable anybody to pick up the object denoted by the term defined. Definitions are for Nelson, as for most contemporary analytic philosophers, extensional.
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Nelson, L. (2016). Lecture IV. In: A Theory of Philosophical Fallacies. Argumentation Library, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-20783-4_5
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